3 Exercise 1 (10 marks) One step in the manufacture of a certain metal clamp involves the drilling of four holes. In a sample of 150 clamps, the average time needed to complete this step was 72 seconds and the standard deviation was 10 seconds. (a) Find an 87% confidence interval for the mean time needed to complete the step. (b) What is the confidence level of the interval (69, 75)? (c) How many clamps must be sampled so that the width of a 93.5% confidence interval is 3? (d) Find a 96% upper confidence bound for the mean time to complete the step. Exercise 2 (12 marks) As part of the quality-control program for a catalyst manufacturing line, the raw materials (alumina and a binder) are tested for purity. The process requires that the purity of the alumina is to be 85%. A random sample from a recent shipment of alumina yielded the following results (in %): 93.2 87.0 92.1 90.1 87.3 93.6 a) Test the requirements of the catalyst manufacturing line using the appropriate hypothesis test (assume 0.05 ). b) Verify your result in part (a) using the appropriate confidence interval. Exercise 3 (14 marks) Fifty specimens of a new computer chip were tested for speed in a certain application, along with 50 specimens of chips with the old design. The average speed, in MHz, for the new chips was 495.6, and the standard deviation was 19.4. The average speed for the old chips was 481.2, and the standard deviation was 14.3. a) Can you conclude a significant difference in the mean speed between the new and old chips? b) Verify your result in part a) using the appropriate confidence interval. c) A sample of 60 even older chips had an average speed of 391.2 MHz with a standard deviation of 17.2 MHz. Someone claims that the new chips average more than 100 MHz faster than these very old ones. Do the data provide convincing evidence for this claim? Exercise 4 (16 marks) Two methods for measuring the molar heat of fusion of water are being compared. Ten measurements made by method A have a mean of 6.02 kilojoules per mole (kJ/mol) with a standard deviation of 0.02 (kJ/mol). Five measurements made by method B have a mean of 6.00 kJ/mol and a standard deviation of 0.01 kJ/mol. a) Can you conclude that the mean measurements for method A is greater than that of method B? b) Repeat this test based on the knowledge that the population variances were equal. c) Find an 80% two sided confidence interval based on the knowledge of \"equal variances\". Exercise 5 (12 marks) Two microprocessors are compared on a sample of six benchmark codes to determine whether there is a difference in speed. The times (in seconds) used by each processor on each code are given in the following table. Code 1 2 3 4 5 6 Processor A 27.2 18.1 27.2 19.7 24.5 22.1 Processor B 24.1 19.3 26.8 20.1 27.6 29.8 a) Can you conclude that the mean speeds of the two processors differ? b) Verify your result in part a) using the appropriate confidence interval. DUE DATE: THURSDAY, MARCH 23RD BY 3PM IN ANY DROP BOX LABELLED \"PAULA DICATO STAT2800\" LOCATED ON THE 4TH FLOOR OF THE UA BUILDING. ASSIGNMENTS ARE DONE INDIVIDUALLY. LATE ASSIGNMENTS ARE NOT ACCEPTED. THIS ASSIGNMENT IS TO BE COMPLETED ENTIRELY BY HAND